Bollobas and Gyarfas conjectured that for n 〉 4（k - 1） every 2-edge-coloring of Kn contains a monochromatic k-connected subgraph with at least n - 2k ＋ 2 vertices. Liu, et al. proved that the conjecture holds when...Bollobas and Gyarfas conjectured that for n 〉 4（k - 1） every 2-edge-coloring of Kn contains a monochromatic k-connected subgraph with at least n - 2k ＋ 2 vertices. Liu, et al. proved that the conjecture holds when n 〉 13k - 15. In this note, we characterize all the 2-edge-colorings of Kn where each monochromatic k-connected subgraph has at most n - 2k ＋ 2 vertices for n ≥ 13k - 15.展开更多
With the development of information technology, the amount of power grid topology data has gradually increased. Therefore, accurate querying of this data has become particularly important. Several researchers have cho...With the development of information technology, the amount of power grid topology data has gradually increased. Therefore, accurate querying of this data has become particularly important. Several researchers have chosen different indexing methods in the filtering stage to obtain more optimized query results because currently there is no uniform and efficient indexing mechanism that achieves good query results. In the traditional algorithm, the hash table for index storage is prone to "collision" problems, which decrease the index construction efficiency. Aiming at the problem of quick index entry, based on the construction of frequent subgraph indexes, a method of serialized storage optimization based on multiple hash tables is proposed. This method mainly uses the exploration sequence to make the keywords evenly distributed; it avoids conflicts of the stored procedure and performs a quick search of the index. The proposed algorithm mainly adopts the "filterverify" mechanism; in the filtering stage, the index is first established offline, and then the frequent subgraphs are found using the "contains logic" rule to obtain the candidate set. Experimental results show that this method can reduce the time and scale of candidate set generation and improve query efficiency.展开更多
The definition of the ascending subgraph decomposition was given by Alavi. It has been conjectured that every graph of positive size has an ascending subgraph decomposition. In this paper it is proved that the regular...The definition of the ascending subgraph decomposition was given by Alavi. It has been conjectured that every graph of positive size has an ascending subgraph decomposition. In this paper it is proved that the regular graphs under some conditions do have an ascending subgraph decomposition.展开更多
Subgraph matching problem is identifying a target subgraph in a graph. Graph neural network (GNN) is an artificial neural network model which is capable of processing general types of graph structured data. A graph ma...Subgraph matching problem is identifying a target subgraph in a graph. Graph neural network (GNN) is an artificial neural network model which is capable of processing general types of graph structured data. A graph may contain many subgraphs isomorphic to a given target graph. In this paper GNN is modeled to identify a subgraph that matches the target graph along with its characteristics. The simulation results show that GNN is capable of identifying a target sub-graph in a graph.展开更多
High-throughput techniques,such as the yeast-two-hybrid system,produce mass protein-protein interaction data. The new technique makes it possible to predict protein complexes by com-putation. A novel method,named DSDA...High-throughput techniques,such as the yeast-two-hybrid system,produce mass protein-protein interaction data. The new technique makes it possible to predict protein complexes by com-putation. A novel method,named DSDA,has been put forward to predict protein complexes via dense subgraph because the proteins among a protein complex have a much tighter relation among them than with others. This method chooses a node with its neighbors to form the initial subgraph,and chooses a node which has the tightest relation with the subgraph according to greedy strategy,then the chosen node is added into the initial subgraph until the subgraph density is below the threshold value. The ob-tained subgraph is then removed from the network and the process continues until no subgraph can be detected. Compared with other algorithms,DSDA can predict not only non-overlap protein com-plexes but also overlap protein complexes. The experiment results show that DSDA predict as many protein complexes as possible. And in Y78K network the accuracy of DSDA is as twice times as that of RNSC and MCL.展开更多
Alavi and his fellows defined the concept of ascending subgraph decomposition of a graph and conjectured that every graph with positive size has an ascending subgraph decomposition in paper [1]. Paper [2] proved that ...Alavi and his fellows defined the concept of ascending subgraph decomposition of a graph and conjectured that every graph with positive size has an ascending subgraph decomposition in paper [1]. Paper [2] proved that K n-R n-1 has a star ascending subgraph decomposition,here K n is the complete graph with order n and R n-1 is a subgraph of K n with size at most n-1. In paper [3],Ma Kejie and Chen Huaitang proved that K n-R n has an ascending subgraph decomposition when the size of R n is not greater than n. In this paper we will prove K n-R has an ascending subgraph decomposition when the size of R is less than 3n/2. This paper will also give the concept of comet and prove that K n-R n-1 has a comet ascending subgraph decomposition.展开更多
Mining subgraphs with interesting structural properties from networks (or graphs) is a computationally challenging task. In this paper, we propose two algorithms for enumerating all connected induced subgraphs of a gi...Mining subgraphs with interesting structural properties from networks (or graphs) is a computationally challenging task. In this paper, we propose two algorithms for enumerating all connected induced subgraphs of a given cardinality from networks (or connected undirected graphs in networks). The first algorithm is a variant of a previous wellknown algorithm. The algorithm enumerates all connected induced subgraphs of cardinality k in a bottom-up manner. Thedata structures that lead to unit time element checking and linear space are presented. Different from previous algorithmsthat work in either a bottom-up manner or a reverse search manner, an algorithm that enumerates all connected inducedsubgraphs of cardinality k in a top-down manner is proposed. The correctness and complexity of the top-down algorithmare theoretically analyzed and proven. In the experiments, we evaluate the efficiency of the algorithms using a set of realworld networks from various fields. Experimental results show that the variant bottom-up algorithm outperforms thestate-of-the-art algorithms for enumerating connected induced subgraphs of small cardinality, and the top-down algorithmcan achieve an order of magnitude speedup over the state-of-the-art algorithms for enumerating connected induced subgraphs of large cardinality.展开更多
Graphs have been widely used in fields ranging from chemical informatics to social network analysis.Graph-related problems become increasingly significant,with subgraph matching standing out as one of the most challen...Graphs have been widely used in fields ranging from chemical informatics to social network analysis.Graph-related problems become increasingly significant,with subgraph matching standing out as one of the most challenging tasks.The goal of subgraph matching is to find all subgraphs in the data graph that are isomorphic to the query graph.Traditional methods mostly rely on search strategies with high computational complexity and are hard to apply to large-scale real datasets.With the advent of graph neural networks(GNNs),researchers have turned to GNNs to address subgraph matching problems.However,the multi-attributed features on nodes and edges are overlooked during the learning of graphs,which causes inaccurate results in real-world scenarios.To tackle this problem,we propose a novel model called subgraph matching on multi-attributed graph network(SGMAN).SGMAN first utilizes improved line graphs to capture node and edge features.Then,SGMAN integrates GNN and contrastive learning(CL)to derive graph representation embeddings and calculate the matching matrix to represent the matching results.We conduct experiments on public datasets,and the results affirm the superior performance of our model.展开更多
Currently,most existing inductive relation prediction approaches are based on subgraph structures,with subgraph features extracted using graph neural networks to predict relations.However,subgraphs may contain disconn...Currently,most existing inductive relation prediction approaches are based on subgraph structures,with subgraph features extracted using graph neural networks to predict relations.However,subgraphs may contain disconnected regions,which usually represent different semantic ranges.Because not all semantic information about the regions is helpful in relation prediction,we propose a relation prediction model based on a disentangled subgraph structure and implement a feature updating approach based on relevant semantic aggregation.To indirectly achieve the disentangled subgraph structure from a semantic perspective,the mapping of entity features into different semantic spaces and the aggregation of related semantics on each semantic space are updated.The disentangled model can focus on features having higher semantic relevance in the prediction,thus addressing a problem with existing approaches,which ignore the semantic differences in different subgraph structures.Furthermore,using a gated recurrent neural network,this model enhances the features of entities by sorting them by distance and extracting the path information in the subgraphs.Experimentally,it is shown that when there are numerous disconnected regions in the subgraph,our model outperforms existing mainstream models in terms of both Area Under the Curve-Precision-Recall(AUC-PR)and Hits@10.Experiments prove that semantic differences in the knowledge graph can be effectively distinguished and verify the effectiveness of this method.展开更多
The problem of subgraph matching is one fundamental issue in graph search,which is NP-Complete problem.Recently,subgraph matching has become a popular research topic in the field of knowledge graph analysis,which has ...The problem of subgraph matching is one fundamental issue in graph search,which is NP-Complete problem.Recently,subgraph matching has become a popular research topic in the field of knowledge graph analysis,which has a wide range of applications including question answering and semantic search.In this paper,we study the problem of subgraph matching on knowledge graph.Specifically,given a query graph q and a data graph G,the problem of subgraph matching is to conduct all possible subgraph isomorphic mappings of q on G.Knowledge graph is formed as a directed labeled multi-graph having multiple edges between a pair of vertices and it has more dense semantic and structural features than general graph.To accelerate subgraph matching on knowledge graph,we propose a novel subgraph matching algorithm based on subgraph index for knowledge graph,called as FGqT-Match.The subgraph matching algorithm consists of two key designs.One design is a subgraph index of matching-driven flow graph(FGqT),which reduces redundant calculations in advance.Another design is a multi-label weight matrix,which evaluates a near-optimal matching tree for minimizing the intermediate candidates.With the aid of these two key designs,all subgraph isomorphic mappings are quickly conducted only by traversing FGqj.Extensive empirical studies on real and synthetic graphs demonstrate that our techniques outperform the state-of-the-art algorithms.展开更多
Rumor Control(RC),aimed at minimizing the spread of rumors in social networks,is of paramount importance,as the spread of rumors can lead to significant economic losses,societal disruptions,and even widespread panic.T...Rumor Control(RC),aimed at minimizing the spread of rumors in social networks,is of paramount importance,as the spread of rumors can lead to significant economic losses,societal disruptions,and even widespread panic.The RC problem has garnered extensive research attention,however,most existing solutions for rumor control face a trade-off between efficiency and effectiveness,which limits their practical application in real-world scenarios.In this light,this paper studies the Truth-spreading-based Rumor Control(TRC)problem,and introduces the Subgraphbased Greedy algorithm Optimized with CELF(SGOC),which employs subgraph techniques and the CELF strategy,as the basic solution for the TRC problem.To improve the performance of SGOC,we carefully design a shortest path length dictionary SPR and an Immune Nodes Set(INS),leading to the Shortest Path-Based Rumor Control(SPRC)algorithm.To further enhance the SPRC algorithm,we develop a pruning method that accelerates the construction process of INS,proposing the Improved Shortest Path-Based Rumor Control(ISPRC)algorithm,which demonstrates superior efficiency compared to both SPRC and SGOC.Extensive experiments conducted on five real-world datasets,demonstrate the effectiveness and efficiency of the proposed algorithms.展开更多
针对知识推理模型在捕获实体之间的复杂语义特征方面难以捕捉多层次语义信息,同时未考虑单一路径的可解释性对正确答案的影响权重不同等问题,提出一种融合路径与子图特征的知识图谱(KG)多跳推理模型PSHAM(Hierarchical Attention Model ...针对知识推理模型在捕获实体之间的复杂语义特征方面难以捕捉多层次语义信息,同时未考虑单一路径的可解释性对正确答案的影响权重不同等问题,提出一种融合路径与子图特征的知识图谱(KG)多跳推理模型PSHAM(Hierarchical Attention Model fusing Path-Subgraph features)。PS-HAM将实体邻域信息与连接路径信息进行融合,并针对不同路径探索多粒度的特征。首先,使用路径级特征提取模块提取每个实体对之间的连接路径,并采用分层注意力机制捕获不同粒度的信息,且将这些信息作为路径级的表示;其次,使用子图特征提取模块通过关系图卷积网络(RGCN)聚合实体的邻域信息;最后,使用路径-子图特征融合模块对路径级与子图级特征向量进行融合,以实现融合推理。在两个公开数据集上进行实验的结果表明,PS-HAM在指标平均倒数秩(MRR)和Hit@k(k=1,3,10)上的性能均存在有效提升。对于指标MRR,与MemoryPath模型相比,PS-HAM在FB15k-237和WN18RR数据集上分别提升了1.5和1.2个百分点。同时,对子图跳数进行的参数验证的结果表明,PS-HAM在两个数据集上都在子图跳数在3时推理效果达到最佳。展开更多
基金Supported by the National Natural Science Foundation of China(10701065 and 11101378)Zhejiang Provincial Natural Science Foundation(LY14A010009)
文摘Bollobas and Gyarfas conjectured that for n 〉 4（k - 1） every 2-edge-coloring of Kn contains a monochromatic k-connected subgraph with at least n - 2k ＋ 2 vertices. Liu, et al. proved that the conjecture holds when n 〉 13k - 15. In this note, we characterize all the 2-edge-colorings of Kn where each monochromatic k-connected subgraph has at most n - 2k ＋ 2 vertices for n ≥ 13k - 15.
基金supported by the State Grid Science and Technology Project (Title: Research on High Performance Analysis Technology of Power Grid GIS Topology Based on Graph Database, 5455HJ160005)
文摘With the development of information technology, the amount of power grid topology data has gradually increased. Therefore, accurate querying of this data has become particularly important. Several researchers have chosen different indexing methods in the filtering stage to obtain more optimized query results because currently there is no uniform and efficient indexing mechanism that achieves good query results. In the traditional algorithm, the hash table for index storage is prone to "collision" problems, which decrease the index construction efficiency. Aiming at the problem of quick index entry, based on the construction of frequent subgraph indexes, a method of serialized storage optimization based on multiple hash tables is proposed. This method mainly uses the exploration sequence to make the keywords evenly distributed; it avoids conflicts of the stored procedure and performs a quick search of the index. The proposed algorithm mainly adopts the "filterverify" mechanism; in the filtering stage, the index is first established offline, and then the frequent subgraphs are found using the "contains logic" rule to obtain the candidate set. Experimental results show that this method can reduce the time and scale of candidate set generation and improve query efficiency.
文摘The definition of the ascending subgraph decomposition was given by Alavi. It has been conjectured that every graph of positive size has an ascending subgraph decomposition. In this paper it is proved that the regular graphs under some conditions do have an ascending subgraph decomposition.
文摘Subgraph matching problem is identifying a target subgraph in a graph. Graph neural network (GNN) is an artificial neural network model which is capable of processing general types of graph structured data. A graph may contain many subgraphs isomorphic to a given target graph. In this paper GNN is modeled to identify a subgraph that matches the target graph along with its characteristics. The simulation results show that GNN is capable of identifying a target sub-graph in a graph.
基金Supported by the National Natural Science Foundation of China (60803025)
文摘High-throughput techniques,such as the yeast-two-hybrid system,produce mass protein-protein interaction data. The new technique makes it possible to predict protein complexes by com-putation. A novel method,named DSDA,has been put forward to predict protein complexes via dense subgraph because the proteins among a protein complex have a much tighter relation among them than with others. This method chooses a node with its neighbors to form the initial subgraph,and chooses a node which has the tightest relation with the subgraph according to greedy strategy,then the chosen node is added into the initial subgraph until the subgraph density is below the threshold value. The ob-tained subgraph is then removed from the network and the process continues until no subgraph can be detected. Compared with other algorithms,DSDA can predict not only non-overlap protein com-plexes but also overlap protein complexes. The experiment results show that DSDA predict as many protein complexes as possible. And in Y78K network the accuracy of DSDA is as twice times as that of RNSC and MCL.
文摘Alavi and his fellows defined the concept of ascending subgraph decomposition of a graph and conjectured that every graph with positive size has an ascending subgraph decomposition in paper [1]. Paper [2] proved that K n-R n-1 has a star ascending subgraph decomposition,here K n is the complete graph with order n and R n-1 is a subgraph of K n with size at most n-1. In paper [3],Ma Kejie and Chen Huaitang proved that K n-R n has an ascending subgraph decomposition when the size of R n is not greater than n. In this paper we will prove K n-R has an ascending subgraph decomposition when the size of R is less than 3n/2. This paper will also give the concept of comet and prove that K n-R n-1 has a comet ascending subgraph decomposition.
基金supported by the National Natural Science Foundation of China under Grant No.61404069the Scientific Research Project of Colleges and Universities in Guangdong Province of China under Grant No.2021ZDZX1027+1 种基金the Guangdong Basic and Applied Basic Research Foundation under Grant Nos.2022A1515110712 and 2023A1515010077the STU Scientific Research Foundation for Talents under Grant Nos.NTF20016 and NTF20017.
文摘Mining subgraphs with interesting structural properties from networks (or graphs) is a computationally challenging task. In this paper, we propose two algorithms for enumerating all connected induced subgraphs of a given cardinality from networks (or connected undirected graphs in networks). The first algorithm is a variant of a previous wellknown algorithm. The algorithm enumerates all connected induced subgraphs of cardinality k in a bottom-up manner. Thedata structures that lead to unit time element checking and linear space are presented. Different from previous algorithmsthat work in either a bottom-up manner or a reverse search manner, an algorithm that enumerates all connected inducedsubgraphs of cardinality k in a top-down manner is proposed. The correctness and complexity of the top-down algorithmare theoretically analyzed and proven. In the experiments, we evaluate the efficiency of the algorithms using a set of realworld networks from various fields. Experimental results show that the variant bottom-up algorithm outperforms thestate-of-the-art algorithms for enumerating connected induced subgraphs of small cardinality, and the top-down algorithmcan achieve an order of magnitude speedup over the state-of-the-art algorithms for enumerating connected induced subgraphs of large cardinality.
文摘Graphs have been widely used in fields ranging from chemical informatics to social network analysis.Graph-related problems become increasingly significant,with subgraph matching standing out as one of the most challenging tasks.The goal of subgraph matching is to find all subgraphs in the data graph that are isomorphic to the query graph.Traditional methods mostly rely on search strategies with high computational complexity and are hard to apply to large-scale real datasets.With the advent of graph neural networks(GNNs),researchers have turned to GNNs to address subgraph matching problems.However,the multi-attributed features on nodes and edges are overlooked during the learning of graphs,which causes inaccurate results in real-world scenarios.To tackle this problem,we propose a novel model called subgraph matching on multi-attributed graph network(SGMAN).SGMAN first utilizes improved line graphs to capture node and edge features.Then,SGMAN integrates GNN and contrastive learning(CL)to derive graph representation embeddings and calculate the matching matrix to represent the matching results.We conduct experiments on public datasets,and the results affirm the superior performance of our model.
基金supported by the National Natural Science Foundation of China(No.U19A2059)the 2022 Research Foundation of Chengdu Textile College(No.X22032161).
文摘Currently,most existing inductive relation prediction approaches are based on subgraph structures,with subgraph features extracted using graph neural networks to predict relations.However,subgraphs may contain disconnected regions,which usually represent different semantic ranges.Because not all semantic information about the regions is helpful in relation prediction,we propose a relation prediction model based on a disentangled subgraph structure and implement a feature updating approach based on relevant semantic aggregation.To indirectly achieve the disentangled subgraph structure from a semantic perspective,the mapping of entity features into different semantic spaces and the aggregation of related semantics on each semantic space are updated.The disentangled model can focus on features having higher semantic relevance in the prediction,thus addressing a problem with existing approaches,which ignore the semantic differences in different subgraph structures.Furthermore,using a gated recurrent neural network,this model enhances the features of entities by sorting them by distance and extracting the path information in the subgraphs.Experimentally,it is shown that when there are numerous disconnected regions in the subgraph,our model outperforms existing mainstream models in terms of both Area Under the Curve-Precision-Recall(AUC-PR)and Hits@10.Experiments prove that semantic differences in the knowledge graph can be effectively distinguished and verify the effectiveness of this method.
基金the National Natural Science Foundation of China(Grant Nos.61976032,62002039).
文摘The problem of subgraph matching is one fundamental issue in graph search,which is NP-Complete problem.Recently,subgraph matching has become a popular research topic in the field of knowledge graph analysis,which has a wide range of applications including question answering and semantic search.In this paper,we study the problem of subgraph matching on knowledge graph.Specifically,given a query graph q and a data graph G,the problem of subgraph matching is to conduct all possible subgraph isomorphic mappings of q on G.Knowledge graph is formed as a directed labeled multi-graph having multiple edges between a pair of vertices and it has more dense semantic and structural features than general graph.To accelerate subgraph matching on knowledge graph,we propose a novel subgraph matching algorithm based on subgraph index for knowledge graph,called as FGqT-Match.The subgraph matching algorithm consists of two key designs.One design is a subgraph index of matching-driven flow graph(FGqT),which reduces redundant calculations in advance.Another design is a multi-label weight matrix,which evaluates a near-optimal matching tree for minimizing the intermediate candidates.With the aid of these two key designs,all subgraph isomorphic mappings are quickly conducted only by traversing FGqj.Extensive empirical studies on real and synthetic graphs demonstrate that our techniques outperform the state-of-the-art algorithms.
基金partially supported by Research Programs of Henan Science and Technology Department(252102210022,232102210054)Henan Province Key Research and Development Project(231111212000)+2 种基金Henan Center for Out-standingOverseas Scientists(GZS2022011)Henan Province Collaborative Innovation Center of Aeronautics and Astronautics Electronic Information TechnologyHenan International Joint Laboratory of Aerospace Intelligent Technology and Systems.
文摘Rumor Control(RC),aimed at minimizing the spread of rumors in social networks,is of paramount importance,as the spread of rumors can lead to significant economic losses,societal disruptions,and even widespread panic.The RC problem has garnered extensive research attention,however,most existing solutions for rumor control face a trade-off between efficiency and effectiveness,which limits their practical application in real-world scenarios.In this light,this paper studies the Truth-spreading-based Rumor Control(TRC)problem,and introduces the Subgraphbased Greedy algorithm Optimized with CELF(SGOC),which employs subgraph techniques and the CELF strategy,as the basic solution for the TRC problem.To improve the performance of SGOC,we carefully design a shortest path length dictionary SPR and an Immune Nodes Set(INS),leading to the Shortest Path-Based Rumor Control(SPRC)algorithm.To further enhance the SPRC algorithm,we develop a pruning method that accelerates the construction process of INS,proposing the Improved Shortest Path-Based Rumor Control(ISPRC)algorithm,which demonstrates superior efficiency compared to both SPRC and SGOC.Extensive experiments conducted on five real-world datasets,demonstrate the effectiveness and efficiency of the proposed algorithms.
